Fall 2015


Fall 2015 BC-Northeastern Algebraic Geometry Conference

Organized by:
Ana-Maria Castravet, Dawei Chen, Qile Chen, Maksym Fedorchuk, Brian Lehmann, Emanuele Macri, and Alina Marian

When:
September 12, 2015, 10am-5pm

Where:
135 Shillman Hall, Northeastern University

Registration: please register so that we have a headcount for coffee breaks and lunch

Speakers:

Titles and schedule:

 10-11am
 
 11-11:30am
 
 11:30am-12:30pm

 12:30-2pm

 2-3pm

 3-3:30pm
 
 3:30-4:30pm
 Benjamin Schmidt  Ample Divisors on Hilbert Schemes of Points on Surfaces
 
 Coffee break
 

 Brendan Hassett  Failure of stable rationality for conic bundles

 Lunch break

 
Anand Deopurkar  Limits of plane quintics via covers of stacky curves

 Coffee break

 
Jenia Tevelev  The Craighero-Gattazzo surface is simply-connected


Abstracts:


Anand Deopurkar: Limits of plane quintics via covers of stacky curves

Abstract:
Which stable curves are limits of smooth plane curves? I will describe the answer explicitly in the first non-trivial case, namely the case of plane quintics. To do so, we will interpret such a curve in terms of a branched cover, but with a twist: the base of the cover will be a stack. The answer will then follow from a nice compactification of such stacky branched covers.

Brendan Hassett: Failure of stable rationality for conic bundles
Abstract: Consider a smooth complex projective variety, fibered in conics over a rational surface. With a few exceptions, such varieties are not birational to projective space. Using Voisin's approach to the decomposition of the diagonal, we prove that the general such variety is not even stably rational. (Joint with Kresch and Tschinkel.)

Benjamin Schmidt: Ample Divisors on Hilbert Schemes of Points on Surfaces
Abstract: The Hilbert scheme of n points on a smooth projective surface X is a smooth projective variety by a classical result of Fogarty. A natural question about these spaces is what all their ample divisors are. Using derived category techniques by Bayer and Macrì, we describe the nef cones if X has Picard rank 1, irregularity 0 and n is large. Moreover, we compute the nef cones if X is the blow up of the projective plane in 8 general points for any n. This is joint work with Bolognese, Huizenga, Lin, Riedl, Woolf and Zhao originating from the boot camp of the Algebraic Geometry Summer Institute 2015 in Utah.

Jenia Tevelev: The Craighero-Gattazzo surface is simply-connected
Abstract: We show that the Craighero–Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply-connected. This was conjectured by Dolgachev and Werner, who proved that its fundamental group has a trivial profinite completion. The Craighero–Gattazzo surface is the only explicit example of a smooth simply-connected complex surface of geometric genus zero with ample canonical class. We hope that our method will find other applications: to prove a topological fact about a complex surface, we use an algebraic reduction mod p technique and deformation theory. Joint work with Julie Rana and Giancarlo Urzua.